Bruno N. Costa, Florian F. Gunsilius
arXiv 30 Sep 2026 · Econometrics
arXiv:2609.40156 · PDF · Extracted main text
In many statistical settings, the available data and maintained assumptions do not suffice to uniquely identify the model parameters of interest. In such cases, one can only identify sets which are guaranteed to contain the true parameters. These are often characterized through linear programs that optimize over models compatible with the observed data. These programs can be infinite-dimensional in the optimizer and the number of constraints. We provide a unified way to characterize and solve such optimization problems by phrasing them as optimal transport problems on path spaces. This allows us to regularize the problem with an entropy penalty, recasting it as a multi-marginal entropic optimal transport problem, which can be solved efficiently via Sinkhorn iterations. In addition, it allows us to establish convergence of the regularized value to the sharpest bound, derive consistency rates for a plug-in estimator, and obtain asymptotic distribution for approximate bounds. The method is general and accommodates settings ranging from instrumental variable models with continuous variables to welfare estimation in heterogeneous demand models. We verify the statistical and computational properties in simulations and provide an application to demand estimation.
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| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | A. Balke and J. Pearl (1997) Bounds on treatment effects from studies with imperfect compliance | 1.000 | 6 | 4 | 100% |
| 2 | G. Peyré and M. Cuturi Computational optimal transport: With applications to data science | 1.000 | 5 | 3 | 100% |
| 3 | M. Cuturi (2013) Sinkhorn distances: Lightspeed computation of optimal transport | 0.928 | 4 | 3 | 100% |
| 4 | M. Nutz (2022) Introduction to entropic optimal transport | 0.928 | 4 | 3 | 100% |
| 5 | F. Gunsilius (1910) A path-sampling method to partially identify causal effects in instrumental variable models | 0.874 | 5 | 2 | 100% |
| 6 | A. Balke and J. Pearl (1994) Counterfactual probabilities: Computational methods, bounds and applications | 0.843 | 3 | 3 | 100% |
| 7 | J. Tan, J. Blanchet, and V. Syrgkanis (2026) Partial identification of policy-relevant treatment effects with instrumental variables via optimal transport | 0.843 | 3 | 3 | 100% |
| 8 | J. A. Hausman and W. K. Newey (2016) Individual heterogeneity and average welfare | 0.644 | 2 | 2 | 100% |
| 9 | H. Lavenant, S. Zhang, Y.-H. Kim, and G. Schiebinger (2024) Toward a mathematical theory of trajectory inference | 0.644 | 2 | 2 | 100% |
| 10 | G. Schiebinger, J. Shu, M. Tabaka, B. Cleary, V. Subramanian, A. Sol… (2019) Optimal-transport analysis of single-cell gene expression identifies developmental trajectories in reprogramming | 0.644 | 2 | 2 | 100% |
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